<h2>Problem 33</h2>
<div style="color:#666;font-size:80%;">20 December 2002</div><br />
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<p>The fraction <img src="" style="display:none;" alt="^(" /><sup>49</sup><img src="" style="display:none;" alt=")" />/<img src="" style="display:none;" alt="_(" /><sub>98</sub><img src="" style="display:none;" alt=")" /> is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that <img src="" style="display:none;" alt="^(" /><sup>49</sup><img src="" style="display:none;" alt=")" />/<img src="" style="display:none;" alt="_(" /><sub>98</sub><img src="" style="display:none;" alt=")" /> = <img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" />/<img src="" style="display:none;" alt="_(" /><sub>8</sub><img src="" style="display:none;" alt=")" />, which is correct, is obtained by cancelling the 9s.</p>
<p>We shall consider fractions like, <img src="" style="display:none;" alt="^(" /><sup>30</sup><img src="" style="display:none;" alt=")" />/<img src="" style="display:none;" alt="_(" /><sub>50</sub><img src="" style="display:none;" alt=")" /> = <img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" />/<img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" />, to be trivial examples.</p>
<p>There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.</p>
<p>If the product of these four fractions is given in its lowest common terms, find the value of the denominator.</p>

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